Light scattered from an object contains both amplitude and phase information. This amplitude and phase information can be captured on, for example, a photosensitive plate by well-known interference techniques to form a holographic recording, or “hologram”, comprising interference fringes. The “hologram” may be reconstructed by illuminating it with suitable light to form a holographic reconstruction, or replay image, representative of the original object.
It has been found that a holographic reconstruction of acceptable quality can be formed from a “hologram” containing only phase information related to the original object. Such holographic recordings may be referred to as phase-only holograms. Computer-generated holography may numerically simulate the interference process, using Fourier techniques for example, to produce a computer-generated phase-only hologram. A computer-generated phase-only hologram may be used to produce a holographic reconstruction representative of an object.
The term “hologram” therefore relates to the recording which contains information about the object and which can be used to form a reconstruction representative of the object. The hologram may contain information about the object in the frequency, or Fourier, domain.
A computer-generated phase-only hologram may be “pixelated”. That is, the phase-only hologram may be represented on an array of discrete phase elements. Each discrete element may be referred to as a “pixel”. Each pixel may act as a light modulating element such as a phase modulating element. A computer-generated phase-only hologram may therefore be represented on an array of phase modulating elements such as a liquid crystal spatial light modulator (SLM). The SLM may be reflective meaning that modulated light is output from the SLM in reflection.
Each phase modulating element, or pixel, may vary in state to provide a controllable phase delay to light incident on that phase modulating element. An array of phase modulating elements, such as a Liquid Crystal On Silicon (LCOS) SLM, may therefore represent (or “display”) a computationally-determined phase-delay distribution. If the light incident on the array of phase modulating elements is coherent, the light will be modulated with the holographic information, or hologram. The holographic information may be in the frequency, or Fourier, domain.
Alternatively, the phase-delay distribution may be recorded on a kinoform. The word “kinoform” may be used generically to refer to a phase-only holographic recording, or hologram.
The phase delay may be quantised. That is, each pixel may be set at one of a discrete number of phase levels.
The phase-delay distribution may be applied to an incident light wave (by illuminating the LCOS SLM, for example) and reconstructed. The position of the reconstruction in space may be controlled by using an optical Fourier transform lens, to form the holographic reconstruction, or “image”, in the spatial domain. Alternatively, no Fourier transform lens may be needed if the reconstruction takes place in the far-field.
A computer-generated hologram may be calculated in a number of ways, including using algorithms such as Gerchberg-Saxton. The Gerchberg-Saxton algorithm may be used to derive phase information in the Fourier domain from amplitude information in the spatial domain (such as a 2D image). That is, phase information related to the object may be “retrieved” from intensity, or amplitude, only information in the spatial domain. Accordingly, a phase-only holographic representation of an object may be calculated.
The holographic reconstruction may be formed by illuminating the Fourier domain hologram and performing an optical Fourier transform, using a Fourier transform lens, for example, to form an image (holographic reconstruction) at a reply field such as on a screen.
FIG. 1 shows an example of using a reflective SLM, such as a LCOS-SLM, to produce a holographic reconstruction at a replay field location, in accordance with the present disclosure.
A light source (110), for example a laser or laser diode, is disposed to illuminate the SLM (140) via a collimating lens (111). The collimating lens causes a generally planar wavefront of light to become incident on the SLM. The direction of the wavefront is slightly off-normal (e.g. two or three degrees away from being truly orthogonal to the plane of the transparent layer). The arrangement is such that light from the light source is reflected off a mirrored rear surface of the SLM and interacts with a phase-modulating layer to form an exiting wavefront (112). The exiting wavefront (112) is applied to optics including a Fourier transform lens (120), having its focus at a screen (125).
The Fourier transform lens (120) receives a beam of phase-modulated light exiting from the SLM and performs a frequency-space transformation to produce a holographic reconstruction at the screen (125) in the spatial domain.
In this process, the light—in the case of an image projection system, the visible light—from the light source is distributed across the SLM (140), and across the phase modulating layer (i.e. the array of phase modulating elements). Light exiting the phase-modulating layer may be distributed across the replay field. Each pixel of the hologram contributes to the replay image as a whole. That is, there is not a one-to-one correlation between specific points on the replay image and specific phase-modulating elements.
The Gerchberg Saxton algorithm considers the phase retrieval problem when intensity cross-sections of a light beam, IA(x,y) and IB(x,y), in the planes A and B respectively, are known and IA(x,y) and IB(x,y) are related by a single Fourier transform. With the given intensity cross-sections, an approximation to the phase distribution in the planes A and B, ΦA(x,y) and ΦB(x,y) respectively, is found. The Gerchberg-Saxton algorithm finds solutions to this problem by following an iterative process.
The Gerchberg-Saxton algorithm iteratively applies spatial and spectral constraints while repeatedly transferring a data set (amplitude and phase), representative of IA(x,y) and IB(x,y), between the spatial domain and the Fourier (spectral) domain. The spatial and spectral constraints are IA(x,y) and IB(x,y) respectively. The constraints in either the spatial or spectral domain are imposed upon the amplitude of the data set. The corresponding phase information is retrieved through a series of iterations.
A holographic projector may be provided using such technology. Such projectors have found application in head-up displays for vehicles and near-eye devices, for example.
A colour 2D holographic reconstruction can be produced and there are two main methods of achieving this. One of these methods is known as “frame-sequential colour” (FSC). In an FSC system, three lasers are used (red, green and blue) and each laser is fired in succession at the SLM to produce each frame of the video. The colours are cycled (red, green, blue, red, green, blue, etc.) at a fast enough rate such that a human viewer sees a polychromatic image from a combination of the three lasers. Each hologram is therefore colour specific. For example, in a video at 25 frames per second, the first frame would be produced by firing the red laser for 1/75th of a second, then the green laser would be fired for 1/75th of a second, and finally the blue laser would be fired for 1/75th of a second. The next frame would then be produced, starting with the red laser, and so on.
Another alternative method, that will be referred to as “spatially separated colours” (SSC) involves all three lasers being fired at the same time, but taking different optical paths, e.g. each using a different SLM or different spatial areas on the same SLM, and then combining to form the colour image.
An advantage of the SSC (spatially separated colours) method is that the image is brighter due to all three lasers being fired at the same time. However, if due to space limitations it is required to use only one SLM, the surface area of the SLM can be divided into three equal parts, acting in effect as three separate SLMs. The drawback of this is that the quality of each single-colour image is decreased, due to the decrease of SLM surface area available for each monochromatic image. The quality of the polychromatic image is therefore decreased accordingly. The decrease of SLM surface area available means that fewer pixels on the SLM can be used, thus reducing the quality of the image.
Holographic colour display systems suffer from two significant problems. Firstly, a mismatch between the physical size of the different colour holographic reconstructions. Secondly, the composite colour image is of low quality because of a resolution mismatch between the different colour holographic reconstructions.
The present disclosure addresses at least these problems.